In this article, a formal specification and verification of the Rabin public-key scheme in a formal proof system is presented. The idea is to use the two views of cryptographic verification: the computational approach relying on the vocabulary of probability theory and complexity theory and the formal approach based on ideas and techniques from logic and programming languages. A major objective of this article is the presentation of the first computer-proved implementation of the Rabin public-key scheme in Isabelle/HOL. Moreover, we explicate a (computer-proven) formalization of correctness as well as a computer verification of security properties using a straight-forward computation model in Isabelle/HOL. The analysis uses a given database to prove formal properties of our implemented functions with computer support. The main task in designing a practical formalization of correctness as well as efficient computer proofs of security properties is to cope with the complexity of cryptographic proving. We reduce this complexity by exploring a light-weight formalization that enables both appropriate formal definitions as well as efficient formal proofs. Consequently, we get reliable proofs with a minimal error rate augmenting the used database, what provides a formal basis for more computer proof constructions in this area.